A literature review failed to find conclusive evidence testosterone increases strength. The abstract says:
Muscle strength and physical function decrease in older men, as do testosterone levels. Nonetheless, the effects of testosterone replacement therapy on muscle strength and physical function remain inconclusive and equivocal. We conducted a rapid systematic review, the results of which showed that testosterone replacement does not affect muscle strength (measured by hand grip strength and leg muscle strength), although it may increase physical function (measured by the 6-minute walk test, Physical Activity Scale for the Elderly score, and other physical performance tests).